Question

Two bonds, each with a face value of $17000, are redeemable at par in t-years and priced to yield y4 = 10%. Bond 1 has a coupon rate c4 = 11.9% and sells for $18444.21. Bond 2 has coupon rate c4 = 4.1% and sells for $ P. What is the value of P?

Answer 1

Step 1: Calculation of t

Yield To Maturity(YTM) = (interest per period+ ((Redemption price - Current market price) / life remaining to maturity)) / ((.4*Redemption price)+ (.6*Current market price))

.10 = ((17000*11.9%)+((17000-18444.21)/t)) / (.4*17000+.6*18444.21)

= (2023+(-1444.21/t)) / 17866.526

(2023+(-1444.21/t)) = .10*17866.526

= 1786.6526

-1444.21/t = 1786.6526-2023 = -236.3474

t = 1444.21/236.3474

= 6.11

Step 2: Calculation of P

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

Prima facie, the bond will trade at discount as YTM>coupon rate

Year	Cash flow	PVAF/PVF@10%	Present Value (Cashflow*PVAF/PVF)
1-6.11	697	4.4141*	3076.65
6.11	17000	0.5586**	9495.98

Current Market Price of Bonds = $\sum$Cashflow*PVAF/PVF

= 3076.65+9495.98

= $12572.63

*PVAF = (1-(1+r)^-n)/r

**PVF = 1 / (1+r)^n